Hello 67BJ8,
I hear ya. I used to put my left hand against the dash top to get leverage so as to pull the choke with my right hand.
The problem maybe the choke cable (moss 734-190) is bending too much under the dash. Try and make that as straight a path as possible. That cable set up is new?
1. Confirm the dash choke cable is as straight as possible.
2. Connect to the remote control cable block. Pull the choke and feel if there is any resistance. There should be a little, because of the inner cable against the outer sleeve and whatever bends in the path under the dash. The choke should be able to pull out and twist to hold in place.
3. Connect the two carb cables to the remote control cable block only. Pull the choke knob to see if any more resistance is added. If the cables are new, there should not be. If there is, there's the problem.
4. Connect both cables to the choke cable brackets. Make sure the metal outer cable sleeves fit down into the bracket opening. You don't want it bending at that junction. Pull the choke knob and feel the resistance.
5. Connect the inner cable to the carb jet housing arm. Pull the choke knob and feel the difference.
6. Connect the springs. You only need enough spring tension to pull the housing arm back when you push the choke knob back in. If the spring pulls too much, it will pull the choke knob back into the dash. You may have to try different springs. I'll attach a photo of my front spring.
The two carb cables should have a black plastic tube over the metal flexible cable. Not sure what it's purpose is other than looks nice and for the reinforcement bracket (moss 372-065) to clamp to, rather than the metal cable sleeve.
I used tri-flow to lubricate the insides of the cable.
Best of luck problem solving. Maybe you'll get lucky and find the under dash cable was bending too much.
Happy Healey Motoring!
Roger